NDSolveUtilitiesA number of utilitiy routines have been written to facilitate the investigation and comparison of various NDSolve methods. These functions have been collected in the package DifferentialEquations`NDSolveUtilities`. Functions provided in the NDSolveUtilities package.This loads the package. In[2]:=  |
A useful means of analysing Runge--Kutta methods is to study how they behave when applied to a scalar linear test problem (see the package NumericalMath`OrderStar` ). This assigns the (exact or infinitely precise) coefficients for the 2 stage implicit Runge--Kutta Gauss method of order 4. In[3]:=  |
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This computes the linear stability function, which corresponds to the (2,2) Padé approximation to the exponential at the origin. In[4]:=  |
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Examples of the functions CompareMethods, FinalSolutions, RungeKuttaLinearStabilityFunction and StepDataPlot can be found within ExplicitRungeKutta . Examples of the function InvariantErrorPlot can be found within Projection . InvariantErrorPlot OptionsThe function InvariantErrorPlot has a number of options that can be used to control the form of the result. Options of the function InvariantErrorPlot. The default value for InvariantDimensions is to determine the dimensions from the structure of the input, Dimensions[invts]. The default value for InvariantErrorFunction is a function to compute the absolute error. The default value for InvariantErrorSampleRate is to sample all points if there are less than 1000 steps taken. Above this threshold a logarithmic sample rate is used.
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